Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8037,2,Mod(1,8037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8037 = 3^{2} \cdot 19 \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8037.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1757681045\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.5476681.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 19x^{3} + 32x^{2} - 44x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2679) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.41126\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8037.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.554958 | −0.392415 | −0.196207 | − | 0.980562i | \(-0.562863\pi\) | ||||
−0.196207 | + | 0.980562i | \(0.562863\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.69202 | −0.846011 | ||||||||
\(5\) | −2.17107 | −0.970934 | −0.485467 | − | 0.874255i | \(-0.661350\pi\) | ||||
−0.485467 | + | 0.874255i | \(0.661350\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41126 | 0.911371 | 0.455685 | − | 0.890141i | \(-0.349394\pi\) | ||||
0.455685 | + | 0.890141i | \(0.349394\pi\) | |||||||
\(8\) | 2.04892 | 0.724402 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.20486 | 0.381009 | ||||||||
\(11\) | 1.55496 | 0.468838 | 0.234419 | − | 0.972136i | \(-0.424681\pi\) | ||||
0.234419 | + | 0.972136i | \(0.424681\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.12216 | −0.311230 | −0.155615 | − | 0.987818i | \(-0.549736\pi\) | ||||
−0.155615 | + | 0.987818i | \(0.549736\pi\) | |||||||
\(14\) | −1.33815 | −0.357635 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.24698 | 0.561745 | ||||||||
\(17\) | 5.71408 | 1.38587 | 0.692934 | − | 0.721001i | \(-0.256318\pi\) | ||||
0.692934 | + | 0.721001i | \(0.256318\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.67350 | 0.821420 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.862937 | −0.183979 | ||||||||
\(23\) | −1.08270 | −0.225758 | −0.112879 | − | 0.993609i | \(-0.536007\pi\) | ||||
−0.112879 | + | 0.993609i | \(0.536007\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.286438 | −0.0572875 | ||||||||
\(26\) | 0.622750 | 0.122131 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.07990 | −0.771030 | ||||||||
\(29\) | 0.609323 | 0.113148 | 0.0565742 | − | 0.998398i | \(-0.481982\pi\) | ||||
0.0565742 | + | 0.998398i | \(0.481982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.39902 | −0.430877 | −0.215438 | − | 0.976517i | \(-0.569118\pi\) | ||||
−0.215438 | + | 0.976517i | \(0.569118\pi\) | |||||||
\(32\) | −5.34481 | −0.944839 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.17107 | −0.543835 | ||||||||
\(35\) | −5.23503 | −0.884881 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.29892 | −1.19994 | −0.599968 | − | 0.800024i | \(-0.704820\pi\) | ||||
−0.599968 | + | 0.800024i | \(0.704820\pi\) | |||||||
\(38\) | 0.554958 | 0.0900261 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.44835 | −0.703346 | ||||||||
\(41\) | −6.12134 | −0.955993 | −0.477996 | − | 0.878362i | \(-0.658637\pi\) | ||||
−0.477996 | + | 0.878362i | \(0.658637\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.93076 | −0.904432 | −0.452216 | − | 0.891908i | \(-0.649366\pi\) | ||||
−0.452216 | + | 0.891908i | \(0.649366\pi\) | |||||||
\(44\) | −2.63102 | −0.396642 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.600852 | 0.0885908 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.18582 | −0.169403 | ||||||||
\(50\) | 0.158961 | 0.0224805 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.89871 | 0.263304 | ||||||||
\(53\) | −8.54484 | −1.17372 | −0.586862 | − | 0.809687i | \(-0.699637\pi\) | ||||
−0.586862 | + | 0.809687i | \(0.699637\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.37593 | −0.455210 | ||||||||
\(56\) | 4.94047 | 0.660199 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.338149 | −0.0444011 | ||||||||
\(59\) | 6.46496 | 0.841666 | 0.420833 | − | 0.907138i | \(-0.361738\pi\) | ||||
0.420833 | + | 0.907138i | \(0.361738\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.93768 | 0.760242 | 0.380121 | − | 0.924937i | \(-0.375882\pi\) | ||||
0.380121 | + | 0.924937i | \(0.375882\pi\) | |||||||
\(62\) | 1.33136 | 0.169082 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.52781 | −0.190976 | ||||||||
\(65\) | 2.43629 | 0.302184 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.887061 | −0.108372 | −0.0541859 | − | 0.998531i | \(-0.517256\pi\) | ||||
−0.0541859 | + | 0.998531i | \(0.517256\pi\) | |||||||
\(68\) | −9.66834 | −1.17246 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.90522 | 0.347240 | ||||||||
\(71\) | 12.6724 | 1.50394 | 0.751970 | − | 0.659198i | \(-0.229104\pi\) | ||||
0.751970 | + | 0.659198i | \(0.229104\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.92007 | −1.04402 | −0.522008 | − | 0.852941i | \(-0.674817\pi\) | ||||
−0.522008 | + | 0.852941i | \(0.674817\pi\) | |||||||
\(74\) | 4.05060 | 0.470872 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.69202 | 0.194088 | ||||||||
\(77\) | 3.74941 | 0.427285 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7821 | 1.66312 | 0.831560 | − | 0.555435i | \(-0.187448\pi\) | ||||
0.831560 | + | 0.555435i | \(0.187448\pi\) | |||||||
\(80\) | −4.87836 | −0.545417 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.39709 | 0.375146 | ||||||||
\(83\) | −3.18414 | −0.349505 | −0.174753 | − | 0.984612i | \(-0.555913\pi\) | ||||
−0.174753 | + | 0.984612i | \(0.555913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.4057 | −1.34559 | ||||||||
\(86\) | 3.29132 | 0.354913 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.18598 | 0.339627 | ||||||||
\(89\) | 13.9012 | 1.47353 | 0.736765 | − | 0.676149i | \(-0.236353\pi\) | ||||
0.736765 | + | 0.676149i | \(0.236353\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70581 | −0.283646 | ||||||||
\(92\) | 1.83195 | 0.190994 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.554958 | −0.0572396 | ||||||||
\(95\) | 2.17107 | 0.222747 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.63568 | 0.775286 | 0.387643 | − | 0.921810i | \(-0.373289\pi\) | ||||
0.387643 | + | 0.921810i | \(0.373289\pi\) | |||||||
\(98\) | 0.658081 | 0.0664763 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.484659 | 0.0484659 | ||||||||
\(101\) | 14.4415 | 1.43698 | 0.718492 | − | 0.695535i | \(-0.244833\pi\) | ||||
0.718492 | + | 0.695535i | \(0.244833\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.49612 | 0.443016 | 0.221508 | − | 0.975159i | \(-0.428902\pi\) | ||||
0.221508 | + | 0.975159i | \(0.428902\pi\) | |||||||
\(104\) | −2.29921 | −0.225456 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.74203 | 0.460587 | ||||||||
\(107\) | 0.462142 | 0.0446769 | 0.0223385 | − | 0.999750i | \(-0.492889\pi\) | ||||
0.0223385 | + | 0.999750i | \(0.492889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.337009 | 0.0322796 | 0.0161398 | − | 0.999870i | \(-0.494862\pi\) | ||||
0.0161398 | + | 0.999870i | \(0.494862\pi\) | |||||||
\(110\) | 1.87350 | 0.178631 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.41805 | 0.511958 | ||||||||
\(113\) | 2.93103 | 0.275728 | 0.137864 | − | 0.990451i | \(-0.455976\pi\) | ||||
0.137864 | + | 0.990451i | \(0.455976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.35062 | 0.219196 | ||||||||
\(116\) | −1.03099 | −0.0957248 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.58778 | −0.330282 | ||||||||
\(119\) | 13.7781 | 1.26304 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.58211 | −0.780191 | ||||||||
\(122\) | −3.29516 | −0.298330 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.05919 | 0.364526 | ||||||||
\(125\) | 11.4772 | 1.02656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4566 | −1.46028 | −0.730142 | − | 0.683295i | \(-0.760546\pi\) | ||||
−0.730142 | + | 0.683295i | \(0.760546\pi\) | |||||||
\(128\) | 11.5375 | 1.01978 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.35204 | −0.118581 | ||||||||
\(131\) | 13.5020 | 1.17968 | 0.589839 | − | 0.807521i | \(-0.299191\pi\) | ||||
0.589839 | + | 0.807521i | \(0.299191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.41126 | −0.209083 | ||||||||
\(134\) | 0.492281 | 0.0425266 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.7077 | 1.00392 | ||||||||
\(137\) | −7.13332 | −0.609440 | −0.304720 | − | 0.952442i | \(-0.598563\pi\) | ||||
−0.304720 | + | 0.952442i | \(0.598563\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.04370 | 0.767077 | 0.383538 | − | 0.923525i | \(-0.374705\pi\) | ||||
0.383538 | + | 0.923525i | \(0.374705\pi\) | |||||||
\(140\) | 8.85778 | 0.748619 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.03266 | −0.590168 | ||||||||
\(143\) | −1.74491 | −0.145916 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.32289 | −0.109860 | ||||||||
\(146\) | 4.95027 | 0.409687 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.3499 | 1.01516 | ||||||||
\(149\) | 7.19506 | 0.589443 | 0.294721 | − | 0.955583i | \(-0.404773\pi\) | ||||
0.294721 | + | 0.955583i | \(0.404773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5275 | −1.10085 | −0.550424 | − | 0.834885i | \(-0.685534\pi\) | ||||
−0.550424 | + | 0.834885i | \(0.685534\pi\) | |||||||
\(152\) | −2.04892 | −0.166189 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.08077 | −0.167673 | ||||||||
\(155\) | 5.20845 | 0.418353 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.02659 | −0.480975 | −0.240487 | − | 0.970652i | \(-0.577307\pi\) | ||||
−0.240487 | + | 0.970652i | \(0.577307\pi\) | |||||||
\(158\) | −8.20346 | −0.652633 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11.6040 | 0.917376 | ||||||||
\(161\) | −2.61067 | −0.205749 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0480 | −1.72693 | −0.863464 | − | 0.504410i | \(-0.831710\pi\) | ||||
−0.863464 | + | 0.504410i | \(0.831710\pi\) | |||||||
\(164\) | 10.3574 | 0.808780 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.76707 | 0.137151 | ||||||||
\(167\) | 1.64969 | 0.127657 | 0.0638285 | − | 0.997961i | \(-0.479669\pi\) | ||||
0.0638285 | + | 0.997961i | \(0.479669\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7408 | −0.903136 | ||||||||
\(170\) | 6.88464 | 0.528027 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.0350 | 0.765160 | ||||||||
\(173\) | −15.6391 | −1.18902 | −0.594510 | − | 0.804088i | \(-0.702654\pi\) | ||||
−0.594510 | + | 0.804088i | \(0.702654\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.690676 | −0.0522102 | ||||||||
\(176\) | 3.49396 | 0.263367 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.71461 | −0.578234 | ||||||||
\(179\) | −22.4432 | −1.67748 | −0.838742 | − | 0.544530i | \(-0.816708\pi\) | ||||
−0.838742 | + | 0.544530i | \(0.816708\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.4845 | −1.81992 | −0.909959 | − | 0.414699i | \(-0.863887\pi\) | ||||
−0.909959 | + | 0.414699i | \(0.863887\pi\) | |||||||
\(182\) | 1.50161 | 0.111307 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.21836 | −0.163540 | ||||||||
\(185\) | 15.8465 | 1.16506 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.88515 | 0.649747 | ||||||||
\(188\) | −1.69202 | −0.123403 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.20486 | −0.0874094 | ||||||||
\(191\) | −8.40818 | −0.608394 | −0.304197 | − | 0.952609i | \(-0.598388\pi\) | ||||
−0.304197 | + | 0.952609i | \(0.598388\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2466 | −0.809546 | −0.404773 | − | 0.914417i | \(-0.632650\pi\) | ||||
−0.404773 | + | 0.914417i | \(0.632650\pi\) | |||||||
\(194\) | −4.23748 | −0.304233 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00644 | 0.143317 | ||||||||
\(197\) | −9.27816 | −0.661042 | −0.330521 | − | 0.943799i | \(-0.607224\pi\) | ||||
−0.330521 | + | 0.943799i | \(0.607224\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4479 | 0.811519 | 0.405760 | − | 0.913980i | \(-0.367007\pi\) | ||||
0.405760 | + | 0.913980i | \(0.367007\pi\) | |||||||
\(200\) | −0.586887 | −0.0414992 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.01443 | −0.563894 | ||||||||
\(203\) | 1.46924 | 0.103120 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.2899 | 0.928206 | ||||||||
\(206\) | −2.49516 | −0.173846 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.52146 | −0.174832 | ||||||||
\(209\) | −1.55496 | −0.107559 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7941 | −1.01846 | −0.509232 | − | 0.860629i | \(-0.670071\pi\) | ||||
−0.509232 | + | 0.860629i | \(0.670071\pi\) | |||||||
\(212\) | 14.4581 | 0.992983 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.256469 | −0.0175319 | ||||||||
\(215\) | 12.8761 | 0.878144 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.78466 | −0.392689 | ||||||||
\(218\) | −0.187026 | −0.0126670 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.71214 | 0.385113 | ||||||||
\(221\) | −6.41209 | −0.431324 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.4239 | −0.698036 | −0.349018 | − | 0.937116i | \(-0.613485\pi\) | ||||
−0.349018 | + | 0.937116i | \(0.613485\pi\) | |||||||
\(224\) | −12.8877 | −0.861098 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.62660 | −0.108200 | ||||||||
\(227\) | −25.1619 | −1.67005 | −0.835026 | − | 0.550211i | \(-0.814547\pi\) | ||||
−0.835026 | + | 0.550211i | \(0.814547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.28237 | 0.349069 | 0.174535 | − | 0.984651i | \(-0.444158\pi\) | ||||
0.174535 | + | 0.984651i | \(0.444158\pi\) | |||||||
\(230\) | −1.30449 | −0.0860158 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.24845 | 0.0819649 | ||||||||
\(233\) | −0.574578 | −0.0376418 | −0.0188209 | − | 0.999823i | \(-0.505991\pi\) | ||||
−0.0188209 | + | 0.999823i | \(0.505991\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.17107 | −0.141625 | ||||||||
\(236\) | −10.9389 | −0.712059 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.64629 | −0.495635 | ||||||||
\(239\) | −14.1140 | −0.912959 | −0.456480 | − | 0.889734i | \(-0.650890\pi\) | ||||
−0.456480 | + | 0.889734i | \(0.650890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.65454 | −0.106578 | −0.0532892 | − | 0.998579i | \(-0.516971\pi\) | ||||
−0.0532892 | + | 0.998579i | \(0.516971\pi\) | |||||||
\(242\) | 4.76271 | 0.306159 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.0467 | −0.643173 | ||||||||
\(245\) | 2.57451 | 0.164479 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.12216 | 0.0714011 | ||||||||
\(248\) | −4.91539 | −0.312128 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.36939 | −0.402836 | ||||||||
\(251\) | 21.8280 | 1.37777 | 0.688886 | − | 0.724870i | \(-0.258100\pi\) | ||||
0.688886 | + | 0.724870i | \(0.258100\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.68355 | −0.105844 | ||||||||
\(254\) | 9.13271 | 0.573037 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.34721 | −0.209200 | ||||||||
\(257\) | 0.602480 | 0.0375817 | 0.0187908 | − | 0.999823i | \(-0.494018\pi\) | ||||
0.0187908 | + | 0.999823i | \(0.494018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.5996 | −1.09359 | ||||||||
\(260\) | −4.12225 | −0.255651 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.49306 | −0.462923 | ||||||||
\(263\) | 21.9560 | 1.35387 | 0.676933 | − | 0.736045i | \(-0.263309\pi\) | ||||
0.676933 | + | 0.736045i | \(0.263309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.5515 | 1.13961 | ||||||||
\(266\) | 1.33815 | 0.0820472 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.50093 | 0.0916836 | ||||||||
\(269\) | −7.92100 | −0.482952 | −0.241476 | − | 0.970407i | \(-0.577631\pi\) | ||||
−0.241476 | + | 0.970407i | \(0.577631\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2602 | −0.623262 | −0.311631 | − | 0.950203i | \(-0.600875\pi\) | ||||
−0.311631 | + | 0.950203i | \(0.600875\pi\) | |||||||
\(272\) | 12.8394 | 0.778504 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.95869 | 0.239153 | ||||||||
\(275\) | −0.445399 | −0.0268586 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.50962 | 0.270957 | 0.135478 | − | 0.990780i | \(-0.456743\pi\) | ||||
0.135478 | + | 0.990780i | \(0.456743\pi\) | |||||||
\(278\) | −5.01887 | −0.301012 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.7261 | −0.641009 | ||||||||
\(281\) | 17.8458 | 1.06459 | 0.532295 | − | 0.846559i | \(-0.321330\pi\) | ||||
0.532295 | + | 0.846559i | \(0.321330\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.1685 | 1.08001 | 0.540004 | − | 0.841662i | \(-0.318423\pi\) | ||||
0.540004 | + | 0.841662i | \(0.318423\pi\) | |||||||
\(284\) | −21.4420 | −1.27235 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.968350 | 0.0572597 | ||||||||
\(287\) | −14.7601 | −0.871264 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6507 | 0.920629 | ||||||||
\(290\) | 0.734146 | 0.0431105 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.0929 | 0.883248 | ||||||||
\(293\) | −8.91987 | −0.521105 | −0.260552 | − | 0.965460i | \(-0.583905\pi\) | ||||
−0.260552 | + | 0.965460i | \(0.583905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.0359 | −0.817202 | ||||||||
\(296\) | −14.9549 | −0.869235 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.99296 | −0.231306 | ||||||||
\(299\) | 1.21496 | 0.0702628 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3006 | −0.824273 | ||||||||
\(302\) | 7.50717 | 0.431989 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.24698 | −0.128873 | ||||||||
\(305\) | −12.8911 | −0.738145 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2611 | 1.15636 | 0.578180 | − | 0.815909i | \(-0.303763\pi\) | ||||
0.578180 | + | 0.815909i | \(0.303763\pi\) | |||||||
\(308\) | −6.34408 | −0.361488 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.89047 | −0.164168 | ||||||||
\(311\) | −18.6975 | −1.06024 | −0.530119 | − | 0.847923i | \(-0.677853\pi\) | ||||
−0.530119 | + | 0.847923i | \(0.677853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.9380 | −0.787820 | −0.393910 | − | 0.919149i | \(-0.628878\pi\) | ||||
−0.393910 | + | 0.919149i | \(0.628878\pi\) | |||||||
\(314\) | 3.34451 | 0.188741 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −25.0117 | −1.40702 | ||||||||
\(317\) | −3.17367 | −0.178251 | −0.0891256 | − | 0.996020i | \(-0.528407\pi\) | ||||
−0.0891256 | + | 0.996020i | \(0.528407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.947472 | 0.0530482 | ||||||||
\(320\) | 3.31699 | 0.185425 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.44881 | 0.0807391 | ||||||||
\(323\) | −5.71408 | −0.317940 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.321428 | 0.0178296 | ||||||||
\(326\) | 12.2357 | 0.677672 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.5421 | −0.692523 | ||||||||
\(329\) | 2.41126 | 0.132937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.9695 | 1.64727 | 0.823636 | − | 0.567119i | \(-0.191942\pi\) | ||||
0.823636 | + | 0.567119i | \(0.191942\pi\) | |||||||
\(332\) | 5.38764 | 0.295685 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.915510 | −0.0500945 | ||||||||
\(335\) | 1.92587 | 0.105222 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.2518 | 0.721874 | 0.360937 | − | 0.932590i | \(-0.382457\pi\) | ||||
0.360937 | + | 0.932590i | \(0.382457\pi\) | |||||||
\(338\) | 6.51563 | 0.354404 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20.9907 | 1.13838 | ||||||||
\(341\) | −3.73038 | −0.202011 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7382 | −1.06576 | ||||||||
\(344\) | −12.1516 | −0.655172 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.67905 | 0.466589 | ||||||||
\(347\) | 18.8008 | 1.00928 | 0.504640 | − | 0.863330i | \(-0.331625\pi\) | ||||
0.504640 | + | 0.863330i | \(0.331625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.86566 | 0.313981 | 0.156991 | − | 0.987600i | \(-0.449821\pi\) | ||||
0.156991 | + | 0.987600i | \(0.449821\pi\) | |||||||
\(350\) | 0.383296 | 0.0204880 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.31096 | −0.442976 | ||||||||
\(353\) | 16.1878 | 0.861587 | 0.430794 | − | 0.902450i | \(-0.358234\pi\) | ||||
0.430794 | + | 0.902450i | \(0.358234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.5128 | −1.46023 | ||||||||
\(356\) | −23.5212 | −1.24662 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.4550 | 0.658269 | ||||||||
\(359\) | −7.84290 | −0.413933 | −0.206966 | − | 0.978348i | \(-0.566359\pi\) | ||||
−0.206966 | + | 0.978348i | \(0.566359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 13.5879 | 0.714162 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.57829 | 0.239968 | ||||||||
\(365\) | 19.3661 | 1.01367 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0247 | 1.67168 | 0.835838 | − | 0.548976i | \(-0.184982\pi\) | ||||
0.835838 | + | 0.548976i | \(0.184982\pi\) | |||||||
\(368\) | −2.43280 | −0.126819 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.79414 | −0.457186 | ||||||||
\(371\) | −20.6038 | −1.06970 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.3490 | −0.742961 | −0.371481 | − | 0.928441i | \(-0.621150\pi\) | ||||
−0.371481 | + | 0.928441i | \(0.621150\pi\) | |||||||
\(374\) | −4.93089 | −0.254970 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.04892 | 0.105665 | ||||||||
\(377\) | −0.683756 | −0.0352152 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3470 | 0.736956 | 0.368478 | − | 0.929637i | \(-0.379879\pi\) | ||||
0.368478 | + | 0.929637i | \(0.379879\pi\) | |||||||
\(380\) | −3.67350 | −0.188447 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.66619 | 0.238743 | ||||||||
\(383\) | −18.0149 | −0.920518 | −0.460259 | − | 0.887785i | \(-0.652243\pi\) | ||||
−0.460259 | + | 0.887785i | \(0.652243\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.14025 | −0.414865 | ||||||||
\(386\) | 6.24138 | 0.317678 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.9197 | −0.655900 | ||||||||
\(389\) | −5.50923 | −0.279329 | −0.139665 | − | 0.990199i | \(-0.544602\pi\) | ||||
−0.139665 | + | 0.990199i | \(0.544602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.18662 | −0.312871 | ||||||||
\(392\) | −2.42965 | −0.122716 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.14899 | 0.259402 | ||||||||
\(395\) | −32.0931 | −1.61478 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.6033 | −1.43556 | −0.717779 | − | 0.696271i | \(-0.754841\pi\) | ||||
−0.717779 | + | 0.696271i | \(0.754841\pi\) | |||||||
\(398\) | −6.35310 | −0.318452 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.643620 | −0.0321810 | ||||||||
\(401\) | −31.5073 | −1.57340 | −0.786699 | − | 0.617336i | \(-0.788212\pi\) | ||||
−0.786699 | + | 0.617336i | \(0.788212\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.69208 | 0.134102 | ||||||||
\(404\) | −24.4353 | −1.21570 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.815365 | −0.0404659 | ||||||||
\(407\) | −11.3495 | −0.562575 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.8319 | 0.931175 | 0.465588 | − | 0.885002i | \(-0.345843\pi\) | ||||
0.465588 | + | 0.885002i | \(0.345843\pi\) | |||||||
\(410\) | −7.37533 | −0.364241 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.60753 | −0.374796 | ||||||||
\(413\) | 15.5887 | 0.767070 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.91301 | 0.339346 | ||||||||
\(416\) | 5.99772 | 0.294062 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.862937 | 0.0422076 | ||||||||
\(419\) | −13.6195 | −0.665358 | −0.332679 | − | 0.943040i | \(-0.607953\pi\) | ||||
−0.332679 | + | 0.943040i | \(0.607953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4308 | −0.605842 | −0.302921 | − | 0.953016i | \(-0.597962\pi\) | ||||
−0.302921 | + | 0.953016i | \(0.597962\pi\) | |||||||
\(422\) | 8.21008 | 0.399660 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.5077 | −0.850248 | ||||||||
\(425\) | −1.63673 | −0.0793929 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.3173 | 0.692862 | ||||||||
\(428\) | −0.781954 | −0.0377972 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.14571 | −0.344597 | ||||||||
\(431\) | −19.5788 | −0.943077 | −0.471539 | − | 0.881845i | \(-0.656301\pi\) | ||||
−0.471539 | + | 0.881845i | \(0.656301\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.6960 | −0.562073 | −0.281036 | − | 0.959697i | \(-0.590678\pi\) | ||||
−0.281036 | + | 0.959697i | \(0.590678\pi\) | |||||||
\(434\) | 3.21025 | 0.154097 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.570227 | −0.0273089 | ||||||||
\(437\) | 1.08270 | 0.0517925 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3673 | 0.781169 | 0.390585 | − | 0.920567i | \(-0.372273\pi\) | ||||
0.390585 | + | 0.920567i | \(0.372273\pi\) | |||||||
\(440\) | −6.91700 | −0.329755 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.55844 | 0.169258 | ||||||||
\(443\) | −30.3496 | −1.44195 | −0.720977 | − | 0.692959i | \(-0.756307\pi\) | ||||
−0.720977 | + | 0.692959i | \(0.756307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.1806 | −1.43070 | ||||||||
\(446\) | 5.78483 | 0.273920 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.68395 | −0.174050 | ||||||||
\(449\) | −5.18878 | −0.244874 | −0.122437 | − | 0.992476i | \(-0.539071\pi\) | ||||
−0.122437 | + | 0.992476i | \(0.539071\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.51843 | −0.448205 | ||||||||
\(452\) | −4.95936 | −0.233269 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.9638 | 0.655353 | ||||||||
\(455\) | 5.87452 | 0.275402 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.4738 | −1.00450 | −0.502252 | − | 0.864721i | \(-0.667495\pi\) | ||||
−0.502252 | + | 0.864721i | \(0.667495\pi\) | |||||||
\(458\) | −2.93150 | −0.136980 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.97730 | −0.185442 | ||||||||
\(461\) | 22.7990 | 1.06186 | 0.530928 | − | 0.847417i | \(-0.321843\pi\) | ||||
0.530928 | + | 0.847417i | \(0.321843\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0362 | 1.21001 | 0.605003 | − | 0.796223i | \(-0.293172\pi\) | ||||
0.605003 | + | 0.796223i | \(0.293172\pi\) | |||||||
\(464\) | 1.36914 | 0.0635606 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.318867 | 0.0147712 | ||||||||
\(467\) | −36.1054 | −1.67076 | −0.835379 | − | 0.549674i | \(-0.814752\pi\) | ||||
−0.835379 | + | 0.549674i | \(0.814752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.13893 | −0.0987668 | ||||||||
\(470\) | 1.20486 | 0.0555758 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.2462 | 0.609704 | ||||||||
\(473\) | −9.22208 | −0.424032 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.286438 | 0.0131427 | ||||||||
\(476\) | −23.3129 | −1.06854 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.83268 | 0.358258 | ||||||||
\(479\) | 18.9055 | 0.863812 | 0.431906 | − | 0.901919i | \(-0.357841\pi\) | ||||
0.431906 | + | 0.901919i | \(0.357841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.19053 | 0.373456 | ||||||||
\(482\) | 0.918202 | 0.0418230 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.5211 | 0.660050 | ||||||||
\(485\) | −16.5776 | −0.752751 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.9276 | 1.89992 | 0.949961 | − | 0.312367i | \(-0.101122\pi\) | ||||
0.949961 | + | 0.312367i | \(0.101122\pi\) | |||||||
\(488\) | 12.1658 | 0.550721 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.42874 | −0.0645441 | ||||||||
\(491\) | −20.5547 | −0.927621 | −0.463811 | − | 0.885934i | \(-0.653518\pi\) | ||||
−0.463811 | + | 0.885934i | \(0.653518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.48172 | 0.156809 | ||||||||
\(494\) | −0.622750 | −0.0280188 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.39055 | −0.242043 | ||||||||
\(497\) | 30.5565 | 1.37065 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0538 | 0.450068 | 0.225034 | − | 0.974351i | \(-0.427751\pi\) | ||||
0.225034 | + | 0.974351i | \(0.427751\pi\) | |||||||
\(500\) | −19.4197 | −0.868478 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.1136 | −0.540658 | ||||||||
\(503\) | 11.3391 | 0.505585 | 0.252792 | − | 0.967521i | \(-0.418651\pi\) | ||||
0.252792 | + | 0.967521i | \(0.418651\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.3536 | −1.39522 | ||||||||
\(506\) | 0.934300 | 0.0415347 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 27.8449 | 1.23542 | ||||||||
\(509\) | −28.2990 | −1.25433 | −0.627166 | − | 0.778885i | \(-0.715785\pi\) | ||||
−0.627166 | + | 0.778885i | \(0.715785\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.5086 | −0.951485 | ||||||||
\(512\) | −21.2174 | −0.937687 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.334351 | −0.0147476 | ||||||||
\(515\) | −9.76141 | −0.430139 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.55496 | 0.0683870 | ||||||||
\(518\) | 9.76704 | 0.429139 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.99175 | 0.218903 | ||||||||
\(521\) | −4.81055 | −0.210754 | −0.105377 | − | 0.994432i | \(-0.533605\pi\) | ||||
−0.105377 | + | 0.994432i | \(0.533605\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.5418 | −1.16059 | −0.580297 | − | 0.814405i | \(-0.697063\pi\) | ||||
−0.580297 | + | 0.814405i | \(0.697063\pi\) | |||||||
\(524\) | −22.8457 | −0.998021 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.1847 | −0.531277 | ||||||||
\(527\) | −13.7082 | −0.597138 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.8278 | −0.949033 | ||||||||
\(530\) | −10.2953 | −0.447199 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.07990 | 0.176886 | ||||||||
\(533\) | 6.86910 | 0.297534 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.00334 | −0.0433784 | ||||||||
\(536\) | −1.81751 | −0.0785046 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.39582 | 0.189517 | ||||||||
\(539\) | −1.84390 | −0.0794225 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.4110 | −1.82339 | −0.911697 | − | 0.410864i | \(-0.865227\pi\) | ||||
−0.911697 | + | 0.410864i | \(0.865227\pi\) | |||||||
\(542\) | 5.69398 | 0.244577 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −30.5407 | −1.30942 | ||||||||
\(545\) | −0.731672 | −0.0313414 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.60780 | −0.368043 | −0.184021 | − | 0.982922i | \(-0.558912\pi\) | ||||
−0.184021 | + | 0.982922i | \(0.558912\pi\) | |||||||
\(548\) | 12.0697 | 0.515593 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.247178 | 0.0105397 | ||||||||
\(551\) | −0.609323 | −0.0259580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.6436 | 1.51572 | ||||||||
\(554\) | −2.50265 | −0.106327 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.3021 | −0.648955 | ||||||||
\(557\) | 11.4448 | 0.484931 | 0.242466 | − | 0.970160i | \(-0.422044\pi\) | ||||
0.242466 | + | 0.970160i | \(0.422044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.65524 | 0.281487 | ||||||||
\(560\) | −11.7630 | −0.497077 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.90367 | −0.417761 | ||||||||
\(563\) | −20.6340 | −0.869619 | −0.434809 | − | 0.900523i | \(-0.643184\pi\) | ||||
−0.434809 | + | 0.900523i | \(0.643184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.36348 | −0.267713 | ||||||||
\(566\) | −10.0828 | −0.423811 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.9647 | 1.08946 | ||||||||
\(569\) | 30.9846 | 1.29894 | 0.649470 | − | 0.760387i | \(-0.274991\pi\) | ||||
0.649470 | + | 0.760387i | \(0.274991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.21829 | −0.134681 | −0.0673407 | − | 0.997730i | \(-0.521451\pi\) | ||||
−0.0673407 | + | 0.997730i | \(0.521451\pi\) | |||||||
\(572\) | 2.95242 | 0.123447 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.19126 | 0.341897 | ||||||||
\(575\) | 0.310126 | 0.0129331 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.38475 | 0.307431 | 0.153716 | − | 0.988115i | \(-0.450876\pi\) | ||||
0.153716 | + | 0.988115i | \(0.450876\pi\) | |||||||
\(578\) | −8.68548 | −0.361268 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.23835 | 0.0929424 | ||||||||
\(581\) | −7.67780 | −0.318529 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.2869 | −0.550286 | ||||||||
\(584\) | −18.2765 | −0.756286 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.95016 | 0.204489 | ||||||||
\(587\) | 29.9644 | 1.23676 | 0.618381 | − | 0.785878i | \(-0.287789\pi\) | ||||
0.618381 | + | 0.785878i | \(0.287789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.39902 | 0.0988499 | ||||||||
\(590\) | 7.78934 | 0.320682 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.4005 | −0.674057 | ||||||||
\(593\) | 8.21408 | 0.337312 | 0.168656 | − | 0.985675i | \(-0.446057\pi\) | ||||
0.168656 | + | 0.985675i | \(0.446057\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.9133 | −1.22633 | ||||||||
\(596\) | −12.1742 | −0.498675 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.674250 | −0.0275722 | ||||||||
\(599\) | −7.14594 | −0.291975 | −0.145988 | − | 0.989286i | \(-0.546636\pi\) | ||||
−0.145988 | + | 0.989286i | \(0.546636\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.0946 | −1.10521 | −0.552606 | − | 0.833443i | \(-0.686366\pi\) | ||||
−0.552606 | + | 0.833443i | \(0.686366\pi\) | |||||||
\(602\) | 7.93624 | 0.323457 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22.8887 | 0.931330 | ||||||||
\(605\) | 18.6324 | 0.757514 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.9253 | −1.41757 | −0.708787 | − | 0.705423i | \(-0.750757\pi\) | ||||
−0.708787 | + | 0.705423i | \(0.750757\pi\) | |||||||
\(608\) | 5.34481 | 0.216761 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.15404 | 0.289659 | ||||||||
\(611\) | −1.12216 | −0.0453976 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6878 | −0.472064 | −0.236032 | − | 0.971745i | \(-0.575847\pi\) | ||||
−0.236032 | + | 0.971745i | \(0.575847\pi\) | |||||||
\(614\) | −11.2440 | −0.453773 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.68223 | 0.309526 | ||||||||
\(617\) | −7.48690 | −0.301411 | −0.150706 | − | 0.988579i | \(-0.548155\pi\) | ||||
−0.150706 | + | 0.988579i | \(0.548155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.22620 | −0.210059 | −0.105029 | − | 0.994469i | \(-0.533494\pi\) | ||||
−0.105029 | + | 0.994469i | \(0.533494\pi\) | |||||||
\(620\) | −8.81281 | −0.353931 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.3763 | 0.416053 | ||||||||
\(623\) | 33.5195 | 1.34293 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.4858 | −0.939431 | ||||||||
\(626\) | 7.73498 | 0.309152 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.1971 | 0.406910 | ||||||||
\(629\) | −41.7066 | −1.66295 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.0356 | 0.917033 | 0.458517 | − | 0.888686i | \(-0.348381\pi\) | ||||
0.458517 | + | 0.888686i | \(0.348381\pi\) | |||||||
\(632\) | 30.2874 | 1.20477 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.76125 | 0.0699484 | ||||||||
\(635\) | 35.7284 | 1.41784 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.33068 | 0.0527234 | ||||||||
\(638\) | −0.525807 | −0.0208169 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −25.0488 | −0.990139 | ||||||||
\(641\) | 4.73368 | 0.186969 | 0.0934845 | − | 0.995621i | \(-0.470199\pi\) | ||||
0.0934845 | + | 0.995621i | \(0.470199\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.06886 | −0.199896 | −0.0999481 | − | 0.994993i | \(-0.531868\pi\) | ||||
−0.0999481 | + | 0.994993i | \(0.531868\pi\) | |||||||
\(644\) | 4.41731 | 0.174066 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.17107 | 0.124764 | ||||||||
\(647\) | −36.1324 | −1.42051 | −0.710256 | − | 0.703943i | \(-0.751421\pi\) | ||||
−0.710256 | + | 0.703943i | \(0.751421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0527 | 0.394605 | ||||||||
\(650\) | −0.178379 | −0.00699660 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 37.3056 | 1.46100 | ||||||||
\(653\) | −24.3079 | −0.951240 | −0.475620 | − | 0.879651i | \(-0.657776\pi\) | ||||
−0.475620 | + | 0.879651i | \(0.657776\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.3139 | −1.14539 | ||||||||
\(656\) | −13.7545 | −0.537024 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.33815 | −0.0521665 | ||||||||
\(659\) | −25.5620 | −0.995756 | −0.497878 | − | 0.867247i | \(-0.665887\pi\) | ||||
−0.497878 | + | 0.867247i | \(0.665887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.32231 | −0.245909 | −0.122955 | − | 0.992412i | \(-0.539237\pi\) | ||||
−0.122955 | + | 0.992412i | \(0.539237\pi\) | |||||||
\(662\) | −16.6318 | −0.646414 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.52405 | −0.253182 | ||||||||
\(665\) | 5.23503 | 0.203006 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.659713 | −0.0255442 | ||||||||
\(668\) | −2.79131 | −0.107999 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.06878 | −0.0412906 | ||||||||
\(671\) | 9.23284 | 0.356430 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.6443 | 1.75946 | 0.879730 | − | 0.475474i | \(-0.157723\pi\) | ||||
0.879730 | + | 0.475474i | \(0.157723\pi\) | |||||||
\(674\) | −7.35422 | −0.283274 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.8656 | 0.764063 | ||||||||
\(677\) | −36.7205 | −1.41128 | −0.705641 | − | 0.708570i | \(-0.749341\pi\) | ||||
−0.705641 | + | 0.708570i | \(0.749341\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4116 | 0.706573 | ||||||||
\(680\) | −25.4182 | −0.974744 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.07020 | 0.0792722 | ||||||||
\(683\) | −12.3880 | −0.474015 | −0.237007 | − | 0.971508i | \(-0.576167\pi\) | ||||
−0.237007 | + | 0.971508i | \(0.576167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4870 | 0.591726 | ||||||||
\(686\) | 10.9538 | 0.418220 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.3263 | −0.508060 | ||||||||
\(689\) | 9.58865 | 0.365298 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.1252 | −0.879722 | −0.439861 | − | 0.898066i | \(-0.644972\pi\) | ||||
−0.439861 | + | 0.898066i | \(0.644972\pi\) | |||||||
\(692\) | 26.4617 | 1.00592 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.4337 | −0.396056 | ||||||||
\(695\) | −19.6345 | −0.744781 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.9778 | −1.32488 | ||||||||
\(698\) | −3.25519 | −0.123211 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.16864 | 0.0441704 | ||||||||
\(701\) | 16.2845 | 0.615056 | 0.307528 | − | 0.951539i | \(-0.400498\pi\) | ||||
0.307528 | + | 0.951539i | \(0.400498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.29892 | 0.275284 | ||||||||
\(704\) | −2.37568 | −0.0895369 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.98353 | −0.338100 | ||||||||
\(707\) | 34.8223 | 1.30963 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8960 | 1.01010 | 0.505049 | − | 0.863090i | \(-0.331474\pi\) | ||||
0.505049 | + | 0.863090i | \(0.331474\pi\) | |||||||
\(710\) | 15.2684 | 0.573014 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28.4825 | 1.06743 | ||||||||
\(713\) | 2.59742 | 0.0972740 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.78832 | 0.141675 | ||||||||
\(716\) | 37.9744 | 1.41917 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.35248 | 0.162433 | ||||||||
\(719\) | 30.4185 | 1.13442 | 0.567210 | − | 0.823573i | \(-0.308023\pi\) | ||||
0.567210 | + | 0.823573i | \(0.308023\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.8413 | 0.403752 | ||||||||
\(722\) | −0.554958 | −0.0206534 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 41.4283 | 1.53967 | ||||||||
\(725\) | −0.174533 | −0.00648200 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.6270 | −1.43260 | −0.716298 | − | 0.697795i | \(-0.754165\pi\) | ||||
−0.716298 | + | 0.697795i | \(0.754165\pi\) | |||||||
\(728\) | −5.54399 | −0.205474 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.7474 | −0.397779 | ||||||||
\(731\) | −33.8888 | −1.25342 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.8178 | −1.28602 | −0.643012 | − | 0.765856i | \(-0.722315\pi\) | ||||
−0.643012 | + | 0.765856i | \(0.722315\pi\) | |||||||
\(734\) | −17.7724 | −0.655990 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.78682 | 0.213305 | ||||||||
\(737\) | −1.37934 | −0.0508087 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0830 | 0.628407 | 0.314204 | − | 0.949356i | \(-0.398263\pi\) | ||||
0.314204 | + | 0.949356i | \(0.398263\pi\) | |||||||
\(740\) | −26.8126 | −0.985651 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.4343 | 0.419765 | ||||||||
\(743\) | 40.4746 | 1.48487 | 0.742435 | − | 0.669918i | \(-0.233671\pi\) | ||||
0.742435 | + | 0.669918i | \(0.233671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.6210 | −0.572310 | ||||||||
\(746\) | 7.96308 | 0.291549 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.0339 | −0.549693 | ||||||||
\(749\) | 1.11434 | 0.0407173 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.0783 | −1.75440 | −0.877200 | − | 0.480124i | \(-0.840592\pi\) | ||||
−0.877200 | + | 0.480124i | \(0.840592\pi\) | |||||||
\(752\) | 2.24698 | 0.0819389 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.379456 | 0.0138190 | ||||||||
\(755\) | 29.3691 | 1.06885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0978 | −1.31200 | −0.655999 | − | 0.754762i | \(-0.727753\pi\) | ||||
−0.655999 | + | 0.754762i | \(0.727753\pi\) | |||||||
\(758\) | −7.96198 | −0.289192 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.44835 | 0.161359 | ||||||||
\(761\) | −0.468230 | −0.0169733 | −0.00848667 | − | 0.999964i | \(-0.502701\pi\) | ||||
−0.00848667 | + | 0.999964i | \(0.502701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.812617 | 0.0294187 | ||||||||
\(764\) | 14.2268 | 0.514708 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.99751 | 0.361225 | ||||||||
\(767\) | −7.25470 | −0.261952 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.5572 | −1.85920 | −0.929600 | − | 0.368569i | \(-0.879848\pi\) | ||||
−0.929600 | + | 0.368569i | \(0.879848\pi\) | |||||||
\(770\) | 4.51750 | 0.162799 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.0294 | 0.684885 | ||||||||
\(773\) | −24.2651 | −0.872756 | −0.436378 | − | 0.899763i | \(-0.643739\pi\) | ||||
−0.436378 | + | 0.899763i | \(0.643739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.687170 | 0.0246839 | ||||||||
\(776\) | 15.6449 | 0.561618 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.05739 | 0.109613 | ||||||||
\(779\) | 6.12134 | 0.219320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.7051 | 0.705103 | ||||||||
\(782\) | 3.43332 | 0.122775 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.66452 | −0.0951613 | ||||||||
\(785\) | 13.0842 | 0.466994 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.85684 | 0.351359 | 0.175679 | − | 0.984447i | \(-0.443788\pi\) | ||||
0.175679 | + | 0.984447i | \(0.443788\pi\) | |||||||
\(788\) | 15.6988 | 0.559248 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.8103 | 0.633663 | ||||||||
\(791\) | 7.06747 | 0.251290 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.66301 | −0.236610 | ||||||||
\(794\) | 15.8736 | 0.563334 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.3701 | −0.686554 | ||||||||
\(797\) | 40.8891 | 1.44837 | 0.724184 | − | 0.689607i | \(-0.242217\pi\) | ||||
0.724184 | + | 0.689607i | \(0.242217\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.71408 | 0.202150 | ||||||||
\(800\) | 1.53096 | 0.0541275 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.4852 | 0.617425 | ||||||||
\(803\) | −13.8703 | −0.489474 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.66795 | 0.199769 | ||||||||
\(806\) | −1.49399 | −0.0526235 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 29.5895 | 1.04095 | ||||||||
\(809\) | −14.1624 | −0.497923 | −0.248961 | − | 0.968513i | \(-0.580089\pi\) | ||||
−0.248961 | + | 0.968513i | \(0.580089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.74292 | 0.307006 | 0.153503 | − | 0.988148i | \(-0.450945\pi\) | ||||
0.153503 | + | 0.988148i | \(0.450945\pi\) | |||||||
\(812\) | −2.48598 | −0.0872408 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.29851 | 0.220763 | ||||||||
\(815\) | 47.8677 | 1.67673 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.93076 | 0.207491 | ||||||||
\(818\) | −10.4509 | −0.365407 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.4868 | −0.785272 | ||||||||
\(821\) | 7.74011 | 0.270132 | 0.135066 | − | 0.990837i | \(-0.456875\pi\) | ||||
0.135066 | + | 0.990837i | \(0.456875\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.5574 | 0.507437 | 0.253719 | − | 0.967278i | \(-0.418346\pi\) | ||||
0.253719 | + | 0.967278i | \(0.418346\pi\) | |||||||
\(824\) | 9.21218 | 0.320922 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.65108 | −0.301010 | ||||||||
\(827\) | −33.0581 | −1.14954 | −0.574772 | − | 0.818314i | \(-0.694909\pi\) | ||||
−0.574772 | + | 0.818314i | \(0.694909\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.1795 | 0.700863 | 0.350431 | − | 0.936588i | \(-0.386035\pi\) | ||||
0.350431 | + | 0.936588i | \(0.386035\pi\) | |||||||
\(830\) | −3.83643 | −0.133165 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.71444 | 0.0594376 | ||||||||
\(833\) | −6.77588 | −0.234770 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.58160 | −0.123947 | ||||||||
\(836\) | 2.63102 | 0.0909958 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.55827 | 0.261096 | ||||||||
\(839\) | −10.2578 | −0.354137 | −0.177068 | − | 0.984199i | \(-0.556661\pi\) | ||||
−0.177068 | + | 0.984199i | \(0.556661\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6287 | −0.987197 | ||||||||
\(842\) | 6.89860 | 0.237741 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.0319 | 0.861632 | ||||||||
\(845\) | 25.4901 | 0.876885 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.6937 | −0.711044 | ||||||||
\(848\) | −19.2001 | −0.659334 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.908315 | 0.0311550 | ||||||||
\(851\) | 7.90253 | 0.270895 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.1505 | −0.963853 | −0.481927 | − | 0.876212i | \(-0.660063\pi\) | ||||
−0.481927 | + | 0.876212i | \(0.660063\pi\) | |||||||
\(854\) | −7.94550 | −0.271889 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.946891 | 0.0323641 | ||||||||
\(857\) | −45.5987 | −1.55762 | −0.778812 | − | 0.627258i | \(-0.784177\pi\) | ||||
−0.778812 | + | 0.627258i | \(0.784177\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.82703 | −0.335294 | −0.167647 | − | 0.985847i | \(-0.553617\pi\) | ||||
−0.167647 | + | 0.985847i | \(0.553617\pi\) | |||||||
\(860\) | −21.7867 | −0.742919 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.8654 | 0.370077 | ||||||||
\(863\) | −38.1966 | −1.30023 | −0.650114 | − | 0.759836i | \(-0.725279\pi\) | ||||
−0.650114 | + | 0.759836i | \(0.725279\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.9537 | 1.15446 | ||||||||
\(866\) | 6.49078 | 0.220566 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.78777 | 0.332219 | ||||||||
\(869\) | 22.9856 | 0.779733 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.995421 | 0.0337286 | ||||||||
\(872\) | 0.690504 | 0.0233834 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.600852 | −0.0203241 | ||||||||
\(875\) | 27.6746 | 0.935573 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.1234 | −0.476914 | −0.238457 | − | 0.971153i | \(-0.576642\pi\) | ||||
−0.238457 | + | 0.971153i | \(0.576642\pi\) | |||||||
\(878\) | −9.08317 | −0.306542 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.58564 | −0.255712 | ||||||||
\(881\) | −12.4137 | −0.418230 | −0.209115 | − | 0.977891i | \(-0.567058\pi\) | ||||
−0.209115 | + | 0.977891i | \(0.567058\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8420 | 0.398514 | 0.199257 | − | 0.979947i | \(-0.436147\pi\) | ||||
0.199257 | + | 0.979947i | \(0.436147\pi\) | |||||||
\(884\) | 10.8494 | 0.364905 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.8428 | 0.565844 | ||||||||
\(887\) | 33.4723 | 1.12389 | 0.561945 | − | 0.827174i | \(-0.310053\pi\) | ||||
0.561945 | + | 0.827174i | \(0.310053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39.6811 | −1.33086 | ||||||||
\(890\) | 16.7490 | 0.561427 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.6375 | 0.590546 | ||||||||
\(893\) | −1.00000 | −0.0334637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.7258 | 1.62873 | ||||||||
\(896\) | 27.8199 | 0.929398 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.87956 | 0.0960921 | ||||||||
\(899\) | −1.46178 | −0.0487530 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.8259 | −1.62663 | ||||||||
\(902\) | 5.28233 | 0.175882 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00543 | 0.199738 | ||||||||
\(905\) | 53.1576 | 1.76702 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.90462 | 0.262469 | 0.131234 | − | 0.991351i | \(-0.458106\pi\) | ||||
0.131234 | + | 0.991351i | \(0.458106\pi\) | |||||||
\(908\) | 42.5744 | 1.41288 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.26011 | −0.108072 | ||||||||
\(911\) | 58.3641 | 1.93369 | 0.966845 | − | 0.255366i | \(-0.0821959\pi\) | ||||
0.966845 | + | 0.255366i | \(0.0821959\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.95121 | −0.163861 | ||||||||
\(914\) | 11.9171 | 0.394182 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.93789 | −0.295316 | ||||||||
\(917\) | 32.5569 | 1.07512 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.3322 | 1.26446 | 0.632231 | − | 0.774780i | \(-0.282139\pi\) | ||||
0.632231 | + | 0.774780i | \(0.282139\pi\) | |||||||
\(920\) | 4.81622 | 0.158786 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.6525 | −0.416688 | ||||||||
\(923\) | −14.2204 | −0.468071 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.09069 | 0.0687413 | ||||||||
\(926\) | −14.4490 | −0.474824 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.25672 | −0.106907 | ||||||||
\(929\) | −14.0042 | −0.459462 | −0.229731 | − | 0.973254i | \(-0.573785\pi\) | ||||
−0.229731 | + | 0.973254i | \(0.573785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.18582 | 0.0388637 | ||||||||
\(932\) | 0.972198 | 0.0318454 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.0370 | 0.655630 | ||||||||
\(935\) | −19.2903 | −0.630861 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.0677 | 0.328897 | 0.164448 | − | 0.986386i | \(-0.447416\pi\) | ||||
0.164448 | + | 0.986386i | \(0.447416\pi\) | |||||||
\(938\) | 1.18702 | 0.0387575 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.67350 | 0.119816 | ||||||||
\(941\) | −25.4924 | −0.831028 | −0.415514 | − | 0.909587i | \(-0.636398\pi\) | ||||
−0.415514 | + | 0.909587i | \(0.636398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.62757 | 0.215823 | ||||||||
\(944\) | 14.5266 | 0.472802 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.11787 | 0.166396 | ||||||||
\(947\) | −10.5429 | −0.342597 | −0.171299 | − | 0.985219i | \(-0.554796\pi\) | ||||
−0.171299 | + | 0.985219i | \(0.554796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0097 | 0.324929 | ||||||||
\(950\) | −0.158961 | −0.00515737 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28.2303 | 0.914948 | ||||||||
\(953\) | 18.5540 | 0.601023 | 0.300511 | − | 0.953778i | \(-0.402843\pi\) | ||||
0.300511 | + | 0.953778i | \(0.402843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.2548 | 0.590711 | ||||||||
\(956\) | 23.8812 | 0.772373 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.4917 | −0.338973 | ||||||||
\(959\) | −17.2003 | −0.555426 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.2447 | −0.814345 | ||||||||
\(962\) | −4.54540 | −0.146550 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.79952 | 0.0901665 | ||||||||
\(965\) | 24.4171 | 0.786016 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.2043 | 1.03562 | 0.517809 | − | 0.855496i | \(-0.326748\pi\) | ||||
0.517809 | + | 0.855496i | \(0.326748\pi\) | |||||||
\(968\) | −17.5840 | −0.565172 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.19989 | 0.295391 | ||||||||
\(971\) | −31.1805 | −1.00063 | −0.500316 | − | 0.865843i | \(-0.666783\pi\) | ||||
−0.500316 | + | 0.865843i | \(0.666783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.8067 | 0.699091 | ||||||||
\(974\) | −23.2681 | −0.745558 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.3418 | 0.427062 | ||||||||
\(977\) | −34.9687 | −1.11875 | −0.559374 | − | 0.828916i | \(-0.688958\pi\) | ||||
−0.559374 | + | 0.828916i | \(0.688958\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.6159 | 0.690846 | ||||||||
\(980\) | −4.35612 | −0.139151 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.4070 | 0.364012 | ||||||||
\(983\) | 46.5994 | 1.48629 | 0.743145 | − | 0.669131i | \(-0.233333\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.1436 | 0.641828 | ||||||||
\(986\) | −1.93221 | −0.0615340 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.89871 | −0.0604061 | ||||||||
\(989\) | 6.42122 | 0.204183 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.7372 | −1.38936 | −0.694679 | − | 0.719320i | \(-0.744453\pi\) | ||||
−0.694679 | + | 0.719320i | \(0.744453\pi\) | |||||||
\(992\) | 12.8223 | 0.407109 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.9576 | −0.537862 | ||||||||
\(995\) | −24.8542 | −0.787932 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.7378 | 1.79691 | 0.898453 | − | 0.439070i | \(-0.144692\pi\) | ||||
0.898453 | + | 0.439070i | \(0.144692\pi\) | |||||||
\(998\) | −5.57941 | −0.176613 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8037.2.a.i.1.3 | 6 | ||
3.2 | odd | 2 | 2679.2.a.i.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2679.2.a.i.1.4 | ✓ | 6 | 3.2 | odd | 2 | ||
8037.2.a.i.1.3 | 6 | 1.1 | even | 1 | trivial |